Evaluation of Smart Split-Range Control Strategies for

Optimized Turbine and Steam Control in Pulp and Paper Plants

Master thesis

by

Eskil Svensson

Student of Sustainable Energy Technology

2019-07-26

i

Abstract

This thesis is about evaluating and improving the performance of a control system.

The control strategy examined is Smart Split-Range Control (SSRC) and guidelines

for best practice are given. Two SSRC systems (C1 and C2) will be designed to

control the simplified steam network of a typical pulp and paper plant. The steam

network has one steam generating HP level and three consumer levels (MP, LP1 and

LP2). The units in the steam network are a boiler, a backpressure turbine and a steam

accumulator between MP and LP2. The priority order for C1 is HP, MP, LP1 and

LP2, while that for C2 is MP, LP1, LP2 and HP. C1 has the inlet control of the

turbine, while C2 uses the backpressure control of the turbine. C1 uses the pressure of

LP2 as MV (manipulated variable) to control the inlet and outlet of the steam

accumulator, while C2 uses the pressure of HP as MV.

The results show that C1 performs better in all the three perspectives consid-

ered (energy, stability and long-term impact). The comparison is complicated due to

the instability of C2, which caused by a few factors: chosen hierarchy of splits, a loop

between SSRCs, control parameters and the difference of inertia (capacity in relation

to net flow) between the pressure levels.

Conclusions are that plants with low inertia on HP level need HP level to be

prioritized and use inlet pressure control of turbine.

Most important future work is to develop a tuning method for SSRC systems.

Secondary is upgrading the model with new SPRV position, dead time, noise,

dynamic linearization and checked control parameters for the boiler.

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Acknowledgements

First, I like to thank God for a lot of things in my life. I want to thank Andrea Toffolo,

my examiner, for having a lot of humour and patience with me. I want to thank Carl

Ressel, my supervisor at Solvina, for being my sounding board and for his patience. I

want to thank Jonas Burström, my friend, for all the support and friendly reminders of

how small this project is in relation to the rest of my life. I want to thank the staff of

Solvina for giving me the opportunity of writing my thesis. Lastly, I want to thank

Isabelle Jalmestig, the love of my life, for all hugs and kind words throughout this

thesis.

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Table of Contents

1 Introduction .......................................................................................................... 1

1.1 Background .................................................................................................... 1

1.1.1 Split-Range Control ................................................................................... 2

1.2 Purpose ........................................................................................................... 3

1.2.1 Objectives ................................................................................................... 3

1.2.2 Limitations ................................................................................................. 3

2 Theoretical Background ...................................................................................... 4

2.1 Dymola ........................................................................................................... 4

2.2 Steam networks .............................................................................................. 4

2.2.1 Steam Boiler ............................................................................................... 4

2.2.2 Backpressure Turbine ................................................................................ 5

2.2.3 Steam Accumulator .................................................................................... 6

2.2.4 Attemperator .............................................................................................. 6

2.2.5 Linear Pressure Control Valve .................................................................. 6

2.3 Transients of a steam network ....................................................................... 8

2.3.1 Board machine start/stop ........................................................................... 8

2.3.2 Batch pulp digester .................................................................................... 8

2.4 Control systems, SRC and SSRC................................................................... 8

2.4.1 PI-controller .............................................................................................. 8

2.4.2 Splitting the signal ..................................................................................... 9

2.4.3 Main and Limiting Control ...................................................................... 11

2.4.4 Deadbands ............................................................................................... 15

2.4.5 Tuning of controller ................................................................................. 16

3 Method ................................................................................................................ 18

3.1 Outlining the model of the typical pulp mill steam network ....................... 18

3.2 Building Dymola Model .............................................................................. 21

3.2.1 Boiler........................................................................................................ 22

3.2.2 Backpressure Turbine .............................................................................. 23

3.2.3 Steam accumulator................................................................................... 24

3.2.4 Pressure Levels ........................................................................................ 24

3.2.5 Attemperators ........................................................................................... 25

3.3 Transients ..................................................................................................... 25

3.4 Building the Controllers ............................................................................... 27

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3.4.1 Building Control system 1 ........................................................................ 27

3.4.2 Building Control system 2 ........................................................................ 28

3.5 Confirmation of behaviour ........................................................................... 29

3.5.1 C1 ............................................................................................................. 30

3.5.2 C2 ............................................................................................................. 30

3.5.3 Tuning of the controllers .......................................................................... 31

3.6 Analysis of the Results................................................................................. 31

4 Result ................................................................................................................... 33

4.1 Energy performance ..................................................................................... 33

4.1.1 KM-stop.................................................................................................... 33

4.1.2 Batch cycle ............................................................................................... 34

4.2 Stability performance ................................................................................... 36

4.2.1 KM-stop.................................................................................................... 36

4.2.2 Batch cycle ............................................................................................... 37

4.3 Long-term impact......................................................................................... 39

4.3.1 KM-stop.................................................................................................... 39

4.3.2 Batch cycle ............................................................................................... 39

5 Discussion............................................................................................................ 40

5.1 Instability ..................................................................................................... 40

5.2 Comments on results .................................................................................... 41

5.3 Desirable results ........................................................................................... 43

5.4 Limitations in setup C2 to establish a model that can be simulated ............ 43

6 Conclusions ......................................................................................................... 44

7 Future work ........................................................................................................ 45

8 References ........................................................................................................... 46

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Denomination

Abbreviations

SRC Split-Range Control

SSRC Smart Split-Range Control

PT Pressure Transmitter

SA Steam Accumulator

SP Set Point

PI Proportional Integral Controller

MV Manipulated Variable

Lim Limiter block

Sub Subtraction block

HL High Limit

LL Low Limit

MC Main Control

LC Limit Control

HLC High Limit Control

LLC Low Limit Control

HP High Pressure

MP Medium Pressure

LP Low Pressure

HC Heat Control (boiler)

PCV Pressure Control Valve

PRV Pressure Relief Valve

SPRV Safety Pressure Relief Valve

SAV Steam Accumulator Valve

TV Turbine Valve

C1 Control system 1

C2 Control system 2

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Symbol Quantity (unit)

Variables

𝐶𝑡 Turbine constant, Stodola equation (-)

𝑃 Pressure (Pa)

𝑇 Temperature (℃)

�̇�𝑡𝑢𝑟𝑏 Turbine mechanical power (MW)

𝜂𝑖𝑠 Isentropic efficiency (%)

ℎ Specific enthalpy (kJ/(kg, K))

𝐾𝑣 Metric valve coefficient (-)

ρ Density (kg/m3)

�̇� Mass flow (kg/s)

�̇�ℎ Mass flow (kg/h)

𝐾𝑐 Proportional gain in a PI-controller (-)

𝜏𝑖 Integral gain in a PI-controller (-)

𝑢 Output of controller (-)

𝑦 Manipulated variable (-)

𝑘 Plant gain (-)

𝜏1 Dominant lag time (s)

𝜃 Time delay (s)

𝜏𝑐 Tuning parameter (-)

�̇� Enthalpy (MW)

�̇� Heat flow (MW)

Indexes

i Inlet

e Exit or outlet

1

1 Introduction

This thesis is about evaluating the performance of a control system operating on the

steam network in a typical pulp and paper plant and improving it from an energy point

of view. This work was performed at Solvina, an active consulting company that for

over 20 years has developed process control for several Swedish and international

industries, including pulp and paper plants. They are striving after best practice soluti-

ons for their customers and this master thesis is a part of their developing strategy.

1.1 Background

A typical pulp and paper plant produce steam at high pressure (HP) levels and

consume it at medium (MP) and low pressure (LP) levels. Together these pressure

levels form a steam network. Units that are typically found in steam networks are

steam boilers, steam accumulators (SA) and backpressure turbines with a few

extractions. Turbines are used to obtain mechanical work from the expansion of steam

between two pressure levels, which otherwise would be lost in direct steam reduction

valves among the pressure levels.

An example of steam network model for a pulp and paper plant can be seen in

Figure 1. Colours represent the different pressure levels of the steam network. Solvina

is developing its own control system architectures to fit costumers’ facilities as well

as possible. A version of Split-Range Control (SRC) is one of the control strategies

being developed for pulp mill steam networks.

Figure 1. Screenshot of a steam network built in Dymola [1]. This example has five pressure levels,

two boilers, a backpressure turbine and a SA. Most pressure levels are connected with pressure

controlling valves.

2

1.1.1 Split-Range Control

A process is usually controlled by outputs from controllers that are operating control

handles. To correct the output signals after the variations induced in the process by

the control handles, input signals are fed back to the controllers from the process. This

is called a closed-loop feedback control [2]. An SRC includes a closed-loop controller

with at least one “split” that distributes the output signal of the controller to different

control handles. The split output signal is determined by the magnitude the total

output signal of the controller [3] and by the defined ranges of the splits (these ranges

may be overlapping). For example, a pressure transmitter (PT in Figure 2) of a steam

network is used as the input to the SRC. Two or more reduction valves (control

handles) opens or closes depending on the split output signal. In the example shown

in Figure 2 the higher of the two pressure levels is used as input to the controller and

the output signal is split over the three reduction valves.

Figure 2. Two pressure levels with connection of valves controlled by split range controller. The

controller uses the red coloured pressure level as the manipulated variable.

The valves, which may be of different size, should open or close when the pressure is

too high or too low, also depending on the position of the valve. The ranges of the

control output signal at operating point 33% may look like in Figure 3. The bigger

range for valve #2 depends on the size compared to that of the other reduction valves.

The purpose of this is to create a linear input response for the controller. In the

example of Figure 2, valve #2 is double the size of valve #1, which is the same size as

valve #3 [4]. The version of SRC that Solvina have made is called “Smart Split-Range

Control” (SSRC) and is described in section 2.

Figure 3. Example of signal graph for valve #1 (yellow), #2 (purple) and #3 (blue). Valve #2 has a

signal range that is double compared to the other valves due to its double size.

3

A steam network has occasionally disturbances as, for instance, pressure drops, spikes

or mass flow-disturbances. The SSRC system is built to suppress the interferences of

a pressure level by manoeuvring the reduction valves to other pressure levels, turbine

inlet or extractions. When the controller tries to stabilize the steam network by

opening the reduction valves a lower mass flow rate of steam flows through the

turbine, resulting in a lower amount of useful mechanical work. Another energy loss

is excess steam vented out to the atmosphere in case of high pressure on the low-

pressure steam header.

Different SSRC systems in relation to a specific steam network setup will result

in different process performances. Steam network characteristics (such as unit

positions, unit sizes and volumes) are expected to affect the choice of the optimal

SSRC setup.

1.2 Purpose

Solvina thinks that there might be more general solutions for implementing their

SSRC setup. Foundational background studies are missing to be able to clearly state

that something really can be optimized or at least refined. The purpose of this thesis is

therefore to find margins of improvement and guidelines for future "best practice"

development of the control strategy.

This thesis is the last step of a master’s degree in Energy Efficiency engineering

in Sustainable Energy Technology. This thesis has therefore the educational purpose

to present an individual work by one student who will practice, develop and display

proficiency in applying theory and method to solve stated problem [5].

1.2.1 Objectives

The first objective is to create a simplified model of a steam network. This model

shall be stable and have a configuration similar to a typical pulp and paper plant.

Smart Split-Range Control is the controller to be built, implemented and variated. A

few indices, listed below, will be compared for the different setups.

• Energy efficiency – Steam vented and electricity generation.

• Stability – Response time, overshoots and oscillations.

• Long-term impact – usage of valves.

1.2.2 Limitations

Several larger limitations have been made to keep the work at a reasonable size,

mainly considering the time frame of 20 weeks. The limitations are:

• The model is built with properties similar to an already existing model in an

older no longer compatible version of Dymola.

• Suitable simplifications for the steam boiler are made.

• Only back pressed turbines will be considered.

• There will be no district heating heat exchangers.

• Only two possible SSRC setups will be evaluated.

4

2 Theoretical Background

This section will cover the theoretical background necessary for this thesis about

modelling, numerical models of steam network units and SSRCs.

2.1 Dymola

Dymola is a simulation tool owned by “Dassault Systemés”. Dymola is based on the

Modelica language, which is a non-proprietary, object oriented, and equation based

language for modelling developed by the Modelica Association [6]. Libraries of

components and units in many different domains may be created by the user of the

basic Modelica library or downloaded [7]. The graphical interface, showing each

component or unit with drag and drop function for placing and connecting them,

makes it easy to build complex systems.

2.2 Steam networks

The steam network consists of several defined units, which are steam boiler,

backpressure turbine, steam accumulator, valves and attemperators. All units consist

of components that are mathematically defined in Dymola. All units are shortly

explained in the following.

2.2.1 Steam Boiler

Boilers are usually one of the essential parts of a typical Rankine cycle in power

plants or other cogeneration systems. Steam pressure and temperature at boiler outlet

have been increased over the years to improve the overall plant efficiency. Boilers

may be classified into a several categories based on, e.g., application, circulation

method, heat source or fuel and whether steam is generated inside or outside the

boiler [8].

A Black Liquor Recovery Boiler is often used in a typical chemical pulp and

paper plant. The boiler utilizes the lignin in the black liquor by-product as fuel and

recovers both heat for steam generation and chemicals for the pulp making process

[9]. Combustion radiation heat and parts or the flue gases heat are used to bring water

close to vapour saturation, step 2a – 3’ orange line, see Figure 4. In the steam drum

saturated vapour is separated from saturated liquid and further transported into the

steam circuit. The vapour is then superheated in one or more steps, step 3’ – 3 red

line, before entering the steam process or steam net. Superheating the vapour again is

called reheating and is usually used in modern Rankine cycle-based power plants to

optimize plant efficiency [10].

5

Figure 4. T-S diagram showing both ideal and actual Rankine cycle, modified from [11]. The “s” in

“2s” and “4s” stands for the isentropic state while the “a”, in “2a” and “4a”, stands for the actual state.

Controlling the level of saturated liquid in the steam drum is critical. Too low

level may expose boiler tubes inside the combustion chamber, leading to overheating

and damage. A too high level may interfere with the separation of vapour phase from

the liquid phase, decrease boiler efficiency and carrying moisture into the process.

Three point feedforward control is a technique suited to handle the feedwater flow

[12].

2.2.2 Backpressure Turbine

Backpressure turbines are used to supply both steam and electricity for facilities and

do not have the final condensing stage. This type of steam turbine is often used to

increase fuel utilization factor in industries such as oil, food and pulp/paper industries,

where a lot of low pressure steam is required [13].

Dymola models a turbine according to Stodola equations. Turbine character-

istics are described by the constant 𝐶𝑡:

𝐶𝑡 =

�̇�𝑛𝑜𝑚𝑖𝑛𝑎𝑙

𝑃𝑖∙ 1/

√1 − (

𝑃𝑒

𝑃𝑖)

2

𝑇𝑖 .

Eq. (1)

The mechanical power, generated �̇�𝑇𝑢𝑟𝑏 is calculated with

�̇�𝑇𝑢𝑟𝑏 = 𝜂𝑖𝑠�̇�(ℎ𝑖 − ℎ𝑒), Eq. (2)

where the isentropic efficiency, 𝜂𝑖𝑠, is defined by

𝜂𝑖𝑠 =ℎ3 − ℎ4

ℎ3 − ℎ4𝑠, Eq. (3)

6

ℎ3 and ℎ4 being the non-ideal turbine process enthalpy for inlet and outlet, respect-

ively. ℎ4𝑠 is the final enthalpy of the isentropic and reversible expansion process [14].

2.2.3 Steam Accumulator

A SA is a pressurized vessel for thermal energy storage containing a composition of

vapour and liquid phase. The SA operates in two ways, steam storage and steam

release. Steam storage occurs when there is a positive pressure difference between

steam source and SA. Figure 5 shows a typical SA with inlets and outlets.

Figure 5. Steam accumulator, or “SA” [15]. The inlet water valves are for filling the SA and the outlet

water valve for emptying it. If a SA is dimensioned properly in a healthy process, neither of the actions

should be necessary.

The storage starts by opening the valve located at the inlet while the valve at the

outlet is closed. The pressure difference drives the steam flow into the SA and, as a

consequence, both pressure and temperature inside the vessel rise. With the new

pressure and temperature, a new equilibrium between the phases is reached with some

vapour changing to liquid.

Steam release occurs when there is a positive pressure difference between the

SA and its outlet. The release process starts by opening the outlet valve while the inlet

valve is closed. The pressure difference drives the steam flow out of the SA. The

pressure inside the vessel drops and a new equilibrium between the phases is reached

with the evaporation of some liquid [15].

2.2.4 Attemperator

Attemperator is a device for temperature control that may injecting water to limit the

temperature of steam. Attemperators uses water from the boiler supply of feed water

[16]. The Dymola model of the attemperator is ideal.

2.2.5 Linear Pressure Control Valve

A valve is a mechanical device that can have one or a few of these tasks:

7

• Stopping/starting fluid flows

• Throttling flows

• Controlling direction of flow

• Controlling/reliving system/process pressure

There are many types of valves for various comb-

inations of tasks. Different types have different

advantages and disadvantages which makes them

useful in different applications. Most valves consist

of an actuator, packing, bonnet, stem, disk, seat and

a body, see Figure 6 [17].

Valve size is described by the 𝐾𝑣 (metric)

value, also called valve coefficient or flow value. 𝐾𝑣

is determined empirically for a specific type of valve,

because of the influence of the specific construction

and design. Other parameters that will affect 𝐾𝑣 are

the physical size and the opening degree of the valve.

𝐾𝑣 is normally quoted for a fully opened valve, with

individual valves for each size [18]. 𝐾𝑣 for steam is

calculated with

𝐾𝑣 =𝑚ℎ̇

37,7 √Δ𝑃 ∙ 𝜌𝑖 , Eq. (4)

where the mass flow, �̇�ℎ, is in kg/h [19].

Valves can differ in how the flow responds to different opening degrees, and the

response is referred to as the inherent flow characteristics of the valve. The different

types of flow characteristics are shown in

Figure 7. Most valves used for control applications have linear, equal percentage

or modified parabolic flow characteristics.

Figure 7. Six different types of flow characteristics [20]. Linear valves are used in this thesis.

Figure 6. Standard parts of a valve

[5]. Valves are used in various tasks.

8

2.3 Transients of a steam network

There are a few typical load transients in a pulp and paper plant. Two steam

consuming units that can make these transients arise are the board machine and the

batch pulp digester.

2.3.1 Board machine start/stop

A board machine is a type of paper machine that produces cardboard. The different

layers of the cardboard are produced up to eight different sheet formations units. Due

to the several sheet formation units, the inner layers of the cardboard can be produced

with cheaper raw materials and the production is easier. When the wet arcs of the

composition are merged the production continues in an ordinary paper machine [21].

The steam and condensate systems, which are present in almost all pulp, paper,

cardboard and tissue machines, are used for drying [22]. Stop and start of a board

machine is one of the most common steam transients of a pulp and paper plant.

2.3.2 Batch pulp digester

Batch pulp digesters are used for the delignification of wood in produce pulp

production. The “Kraft process” is a process where white liquor is used to separate the

cellulose from the undesired lignin contained in wood. Heating stimulates the reaction

and recirculating external heat exchangers are common for this purpose. A certain

Kappa number, which is a measurement to describe the degree of delignification, is

set as the target for the cooking process within the batch digester [23]. The cooking

process is done in batches and steam is commonly used for heating.

2.4 Control systems, SRC and SSRC

SSRC is mostly built out of research through other master theses and previous own

experience by Solvina. Basic control theory and SRC theory are fundamental to

introduce SSRC presented in this section. The example in the introduction is reprised

and additional examples are presented. The aim of this section is to give a basic

understanding of the SSRC.

2.4.1 PI-controller

The main task of a feedback controller is to automatically keep a process at a defined

Setpoint (SP) and suppress interferences from the process. There are a several types

of feedback controllers and the most common controller in the process industry is the

proportional integral (PI) controller. A PI-controller consists of two parts, a propor-

tional part (P-part, 𝐾𝑐) and an integral part (I-part, 𝜏𝑖), see the block diagram in Figure

8. The feedback or manipulated variable (MV), 𝑦(𝑡), is subtracted from the SP, 𝑟(𝑡),

to create the error signal, 𝑒(𝑡), which is multiplied by the P-part and integrated by the

I-part. The sum of these new signals creates the output, 𝑢(𝑡), which is fed to a control

handle (i.e. a valve) in the process. P- and I-parts have two corresponding

characteristic parameters: 𝐾𝑐, the gain, and 𝜏𝑖, the integral time [24].

9

Figure 8. Block diagram of a reverse control PI-controller. PI-controllers are used in a wide range of

applications for automatic process control.

The controller has two ways of respond to an increasing input signal, it can either

increase or decrease the output signal. This is called direct or reversed control,

respectively. Reverse action control has a decreasing output when the MV is

increasing, while direct action control has an increasing output when the MV is

increasing.

Anti-windup is a safety compensation for PI-controllers and other controllers. If the

control signal is operating between its saturation limits, the anti-windup is dormant. If

a saturation limit is reached, the anti-windup is preventing the I-part from being too

large, because that would cause overshoots and limit cycles [25].

2.4.2 Splitting the signal

The “splitting” of the controller signal is taking place after a controller in a so called

“Split”. A simple form of Split consists of a limiter block (Lim i) with high limit (HL)

and low limit (LL), and a subtraction block (Sub i), see Figure 9.

Figure 9. Standard parts of a split. 𝑦𝑖 and 𝑢𝑖+1 are the outputs of the split. Gain i is used to compensate

output 𝑦𝑖if the signal needs to be manipulated further before the control handle.

The split signal can be described with

𝑢𝑖+1 = 𝑢𝑖 − 𝑦𝑖, Eq. (5)

where 𝑢1 either comes directly from the controller itself of from an earlier split,

𝑦𝑠𝑝𝑙𝑖𝑡1 goes to the control handle and 𝑢2 goes to next split if there are more splits.

In the example of Figure 2, an SRC splits the signal over three valves. Figure 10

shows an example in which two splits after the PI-controller result in three possible

output signals of the SRC.

10

Figure 10. PI-controller with 2 splits. The extra gain (split 3) is to scale the 𝑢3 signal to match the input

range of the control handle.

The SRC that splits the signal to the valves of Figure 2 is shown in Figure 11 and is

referred to in the following as split structure 1. The signal out of the PI-controller

goes to both the first subtraction block and Lim 1. The signal going to Valve #1 is

subtracted from the signal of the PI-controller in the first subtraction-block. If the

signal is less than the high limit of the first limiter (in this example 𝑢𝑃𝐼 <25 %) then

the output signal of the first subtraction block is zero. If the signal is above Lim 1’s

max-value (in this example 25%< 𝑢𝑃𝐼) then valve #1 will be completely opened and

𝑢2 > 0. For 𝑛 outputs 𝑛 − 1 Lims are needed.

Figure 11. Signal 𝑢𝑃𝐼 is split in SRC 1/split structure 1. The term “split structure” refers to the splits

and their order. The term “controller” refers to the PI-controller. The term “SRC/SSRC” refers to the

combination of “split structure” and “controller”.

The split structure, i.e. the order of splits in Figure 11, prioritizes which valves should

operate depending on the measurement value. For example, Figure 12 shows split

structure 2, in which a change is made on the controller so that now valve #2 is the

first in the split order.

11

Figure 12. Signal 𝑢𝑃𝐼 is split in split structure 2/SRC 2. Placing Split 2 first causes valve #2 to operate

first.

Split structure 2 with a linearized control system would only utilize valve #2 at the

stated PI-controller output of 𝑢𝑃𝐼 = 33%. The opening degree of valve #2 is then

66%. The corresponding signal graph to this split structure 2, is showed in Figure 13.

Figure 13. Signal graph corresponding to the split structure described in Figure 12. The signal graph

illustrates the different split responses in the range of controller output.

From the examples above it can be concluded that a control signal might be split any

number of times in an SRC by adding a pair of limiter and subtraction blocks.

Depending on the order, the splits will be saturated and the corresponding control

handles operated in a specific order.

2.4.3 Main and Limiting Control

The output of the splits described in the examples of Figure 2, Figure 3 and Figure 11

are directly connected to the valves. The signal “orders” the valves to either be

opened more or closed more and this is called “Main Control” (MC) in this thesis.

The signal split of SSRC reminds of that in SRC, but there are two major differences.

First, the limiter block of a split has variable limits, see Figure 14. Second, in order to

have 𝑛 outputs, 𝑛 Lims are needed, see Figure 15.

12

Figure 14. Split with variable high limit and low limit. HL and LL are two implemented control

handles which are either controlled by another SSRC or set to a specific value.

The MC split is designed to control one control handle in a split structure. Three

control handles are located between two pressure levels in Figure 2. If both those

pressure levels are to be kept constant by a SSRC system, there will be a SSRC for

each pressure level. With the presented theory two SSRC and one operating point (the

three valves between the two pressure levels) will result in a conflict between the two

SSRCs: When SSRC 1 wants to open the valves, the other might want to close them.

To solve this issue variable limits are used, because the limiter blocks can be seen as a

new type of control handles. This means that, even in the case of two pressure levels

and just one handle to control (e.g. a valve), the SSRC system can be satisfied by

controlling MC splits. The splits controlling the limits of MC splits are called Limit

Control (LC) splits in this thesis. These LC splits interact with the MC splits of SSRC

by limiting the input or output from the MC to control handles (see Figure 15), so that

LC split have higher priority in the control hierarchy than the MC split. In fact, this

new possible way of communication and interaction creates a type of SSRC system

that can be described as a hierarchy system.

Figure 15. SSRC system of two PI-controllers with corresponding split structure. SSRC 1 (green)

controls two control handles in the process and SSRC 2 (purple) controls two control handles in SSRC

1. The last splits of both SSRC (MC/H-LC split 2) contain only a Lim and a gain.

The hierarchy is chosen according to the importance and the sensitivity of the

different steam consumers in the controlled steam network. A SSRC with high

priority is in LC of variable HL and LL and may allow or force lower priority MC to

manoeuvre control handles. Changing a HL requires a High Limit Control (HLC) and

changing a LL require a Low Limit Control (LLC).

13

Example

The steam network in Figure 16 consists of a High Pressure (HP) and a Low Pressure

(LP) level. There are two manoeuvre handles to the steam network. Valve #1 is a

pressure control valve (PCV) between HP and LP and valve #2 is a pressure relief

valve (PRV) between LP and the atmosphere. Flow characteristic and 𝐾𝑣 are identical

for the valves.

Figure 16. A steam network consisting of two pressure levels. Valve #1 is a PCV, which reduces steam

from HP to LP. Valve #2 is a PRV that vents steam out of the steam network.

Each pressure level has its own SSRC; HP SSRC is Red, and LP SSRC is Blue. Red

has only LC of Blue, while Blue has MC for both valves (#1 and #2), see Figure 17.

The hierarchy is set so that HP as higher priority and LP lower, and this is realized by

LC splits in Red SSRC linked to the MC split of the valve connecting HP and LP.

Figure 17. The SSRC system of the example in Figure 16. Two physical control handles, the valves,

are operated by LP SSRC (Blue). Two control handles in LP SSRC are controlled by HP SSRC (Red).

The PI-controller of Red have direct signal while the PI-controller of Blue has reverse

signal. The steady state signal graphs of the SSRC system are shown in Figure 18. It

is worth noting that the shape of Blue MC of valve #2 is inverted, i.e. it opens when

the signal is decreasing.

14

Figure 18. Signal graphs for the SSRC system at steady state. MC #2 is inverted to give a full signal

when the controller output is zero and to give no signal when the controller output is < 50%.

If the steady state is disturbed by the tripping of a load in the LP level, an excess of

steam occurs in the LP level. The SSRC system responds in the following way (the

percentages are just for illustration and not a real case):

1. Pressure of LP level increases

a. Signal of Blue decreases

i. Signal of MC #1 decreases

1. Valve #1 closes more

ii. Signal of MC #2 stays at 0%

1. Valve #2 stays closed

2. Pressure of HP level increases

a. Signal of Red increases

i. Signal of LLC increases

1. Valve #1 opens more (minimum opening rises)

ii. Signal of HLC holds at 100%

3. Pressure of LP level rises

a. Signal of Blue decreases

i. Signal of MC #1 holds at minimum opening by the LLC.

1. Valve #1 holds at the minimum opening.

ii. Signal of MC #2 increases

1. Valve #2 opens

4. HP level becomes steady at a pressure different from the initial condition.

15

a. Signal of Red holds at 75%

i. Signal of LLC #1 holds at 50%

1. Valve #1 holds at 50% opening degree

ii. Signal of HLC #1 holds at 100%

5. LP level becomes stable at a pressure different from the initial condition.

a. Signal of Blue holds at 25%

i. Signal of MC #1 holds at 50% (overridden by Red LLC)

1. Valve #1 holds at 50% opening degree

ii. Signal of MC #2 holds at 50%

1. Valve #2 holds at 50% opening degree

In this way a new steady state for the SSRC system is reached, as shown in the signal

graphs of Figure 19.

Figure 19. Signal graph of the SSRC system at the new steady state after the disturbance. As described

in point 5.a.i in the example, Red overrides Blue SSRC with the LLC.

2.4.4 Deadbands

As explained, the LC split of a SSRC is supposed to override another SSRC MC split.

A problem may arise when a MC split has a signal that differs a lot from the controll-

ing LLC split, as in previous example. In Figure 18, the signals of LLC #1 and MC #1

differ by 25% of either PI-controllers maximum output. During the disturbance the

signal of Blue decreases while the signal of Red increases. Still considering Figure 18,

the gap between them creates a range in which no action can occur: the increasing

signal of Red is not having any effect on the system until the LLC split’s signal is

16

higher than the MC split’s signal. This is called a deadband. Deadbands generates

time delays, so that controller outputs become too large due to the time dependent I-

part of the PI-controller, causing in turn over and/or undershoots of the process. This

drawback is addressed in a more advanced type of SSRC. MC splits outputs are fed

back to one of the LC splits limits, depending on whether the LC split is an HLC split

or an LLC split. A (small) percentage of the feedback is either subtracted or added to

the LLC split or to the HLC split, respectively. This is to minimize the deadbands and

make the controller have a faster response [4]. By implementing a 10% difference

(deadband) in the LC-feedback, the signal graph of the previous example (Figure 18)

becomes that illustrated in Figure 20. Another significant feature of this feedback is

that the SSRC can consider the gap occurring when valves are manually taken out of

service during operation.

Figure 20. Signal graph of example in Figure 18 with implemented feedback to the LC split. Red

controller output is 50% and split outputs are 60% for HLC #1 and 40% for LLC #1.

2.4.5 Tuning of controller

Tuning the PID-controllers is a major part of optimizing process systems, but without

a systematic procedure it is very time consuming. There are a lot of methods for this

task, including the test of signal responses related to the process of interest. These

tests can be either setting the controller to manual operation to see how the process

reacts to changes in the controller output or changing the parameters of the controller

with a systematic procedure. An example of the first mentioned methods is the

Lambda-method, an example of the other method is the “Ziegler-Nichols method”

[24]. Another method is the SIMC-method, similar to the Lambda-method: it sets the

17

controller to manual operation to see how the process response to changes in the cont-

roller output. It is developed to

• Be justified, preferably model-based and analytical derived.

• Be simple and easy to memorize.

• Working well on a wide range of processes.

The procedure aims at selecting a tuning parameter, 𝜏𝑐, and estimate the following

model information (which are also shown in Figure 21):

• Plant gain (𝑘) (based on Δ𝑦 and Δ𝑢)

• Dominant lag time, 𝜏1

• Time delay, 𝜃

Figure 21. Step response of a first-order process with time delay (modified from [26]). The information

is used in various tuning procedures.

With estimated model information, 𝑘 is first calculated with

𝑘 =Δ𝑦

Δ𝑢 Eq. (6)

and then, with 𝜏𝑐, 𝜏1, 𝜃 and 𝑘 calculate the 𝐾𝑐 (P-part) of the controller for a first-

order process with

𝐾𝑐 =1

𝑘

𝜏1

𝜏𝑐 + 𝜃 . Eq. (7)

Then 𝜏𝑖 (I-part) of the controller is determined with

𝜏𝑖 = min{𝜏1, 4(𝜏𝑐 + 𝜃)}. Eq. (8)

The new parameters of the process are then implemented.

18

3 Method

This section of the report describes the method used for each task of the thesis work.

The method for building the model and using it to obtain result data is described with

a workflow diagram in Figure 22. The workload of each task is displayed by the size

of the text in the corresponding block.

Figure 22. Workflow diagram describing the method. Simulating the model and making ad hoc fixes

and adjustments were the central part of the work.

A list of steam network units, components and characteristics (such as energy and

mass balances) for the model is chosen using an old model of a real pulp and paper

plant as blueprint. A programmed Excel book (Steam-Tables.xls), with built in steam

table functions by M. Holmgren [27], is used to calculate all thermodynamic quanti-

ties for the stations in the steady state of the model. This information of steady state

flows, pressures and temperatures is used to create the model with Dymola. The

required components and units are either developed within this thesis or taken from

existing Dymola libraries.

A SSRC system, referred to as C1, is built with a priority list that represents a

blueprint for how the SSRC should operate the valves among the different pressure

levels, inlets and extractions of the turbine. The splitting of the output signal is then

validated with operational tests of the model and is finally tuned.

Documented load variations of real pulp and paper plants are scaled to match

model characteristics and implemented in the model to be used as interfering transi-

ents. The resulting electricity generated, frequency of valve usage and vented steam

during and after transient are recorded.

A new controller priority list is developed from the experiences made during the

thesis work and implemented as a new SSRC system, referred to as C2. The new

controller is built and validated in a similar way to the first controller and then tested

against the same transients.

The data of the two different cases are processed and results are compared, ana-

lysed and discussed to draw the conclusion of this thesis.

3.1 Outlining the model of the typical pulp mill steam network

The old model of a pulp and paper plant is used as the blueprint to build a new model

for this thesis. Pressure levels and temperatures for the steam network of old model

19

are shown in Table 1. This old model represents a real plant and was built in an older

version of Dymola, so it could not be reused.

Table 1. Approximate characteristics of the old model of a pulp mill.

Pressure level 𝑝 [bar(a)] 𝑇 [℃]

HP1 111 480

HP2 61 460

MP1 18 230

MP2 13 210

LP1 9 184

LP2 4 146

The old model (Figure 23) consists of three boilers (P11, P12 and SP5), various loads

in each pressure level except for HP and MP1 levels, and a turbine (G6), which has

two inlets and four extractions. PCV are positioned between most of the pressure

levels and there is a SA (“ACKUMULATORN”) positioned between MP2 and LP2.

Figure 23. Overview of old model steam network, showing all the 6 pressure levels conections and the

larger units. The turbine is generating 63 MW in this screenshot.

HP2 and MP2 are removed from the new model in order to narrow down the

complexity of the model and save time. The chosen pressure levels in the steam

20

network of the thesis model are showed in Table 2. Only the HP level is changed from

111 to 101 bar(a), which is in a realistic range for HP levels.

Table 2. Pressures and temperatures of the pressure levels.

Pressure level 𝑝 [bar(a)] 𝑇 [℃]

HP 101 480

MP 13 210

LP 1 9 184

LP 2 4 146

Two boilers are removed in the new model due to the removal of two pressure levels.

The remaining boiler is set to provide steam to the steam network and to the

backpressure turbine with steam. The turbine has extractions for MP, LP1 and LP2.

There is a SA connected between MP and LP2. Most pressure levels are connected to

one another with PCVs, which are control handles for pressure, and attemperators for

correcting the temperatures to the desired values. The units described are assembled

to a simplified steam network shown in Figure 24.

Figure 24. Components and units of the planned new model: Boiler, backpressure turbine, steam

accumulator, loads, valves and attemperators. The valve at the bottom of the figure is a PRV for

venting steam out of the process.

This boiler is supplying steam to HP level, which is in turn distributing steam to other

pressure levels. The mass flow and energy content at boiler outlet are assumed to

equal to the combined steam flows and energy content of pressure levels HP1 and

HP2 in old model, minus the contribution from the MP1 level (that is removed),

21

�̇�𝐻𝑃1 + �̇�𝐻𝑃2 − �̇�𝑀𝑃1 = �̇�𝐻𝑃𝑛𝑒𝑤. Eq. (9)

This assumption has been made to achieve a more realistic model despite the

simplifications introduced. The mass flow is then calculated with

�̇�𝐻𝑃𝑛𝑒𝑤

ℎ101𝑏𝑎𝑟𝑎,480℃= �̇�𝐻𝑃𝑛𝑒𝑤, Eq. (10)

where ℎ101𝑏𝑎𝑟,480℃ is the specific enthalpy for vapour at 101 bar(a) and 480℃. Mass

flow �̇�𝐻𝑃𝑛𝑒𝑤 is used at the beginning of model building as guideline. This assumed

mass flow is used so that the model can have a realistic behaviour.

The steam load average for each pressure level of the new model is decided to

be the same as the old model, see Table 3.

Table 3.Average loads of consumers at all consumer levels.

Pressure level Steam consumption [kg/s]

MP 16,7

LP1 48,2

LP2 42,8

3.2 Building Dymola Model

The boiler is the first unit in the Dymola model. Each pressure level is then inserted

with corresponding turbine stage, from highest to lowest pressure. Each time a new

unit is inserted in the model, boundaries (see “END” in Figure 25) were added that

corresponded to next pressure level, turbine stage or other steam network connection.

The reason of using boundaries during the expansion of the model is to facilitate

model debugging. With a lower number of new components or units inserted before

each simulation, fewer issues are possible if last implementation was successful.

During the building phase PI-controllers are inserted to make model simulations

possible. When all units are in place and assembled into a working model, the

controllers are replaced by the MC splits of the SSRC.

Figure 25. A screenshot of an early building stage of the model. The boiler (red unit) is connected to

the HP pressure level and the valve is a PCV between HP and MP. The PI-controller is controlling the

opening degree of the valve with pressure of the HP as MV.

22

After the first controller is finished, the model is adjusted to reproduce more

accurately the original pressures and temperatures after all units and components are

in place. Most of the adjustments are done in the turbine by changing the isentropic

efficiency, 𝜂𝑖𝑠 to tune extraction temperatures. The procedure starts with the highest

pressure extraction, moving down to the lowest pressure extraction. This is to prevent

unwanted extra steam flows in the model due to the attemperators cooling feature.

The consequence of extra steam in the model would be a larger potential of energy

due to an open system and a possible higher yield of electricity generated. This is

unwanted in the comparison between energetic performance of different controllers.

3.2.1 Boiler

The boiler consists of a feed water source, dome and superheater (two volumes) and

one Heat Control (HC) system, see Figure 26. The feed water source is set to 140 bar

and 45 degrees. The flow is controlled by a three-point feedforward controller which

is not a part of any of the SSRC systems considered later. This control structure uses

the dome level as measurement value and the difference between out and in-flow as

feedforward parameter with inlet valve as control handle [24].

Figure 26. Boiler and Heat Control. The leftmost boundary is the MAVA source, supplying the dome

with water. The dome and superheater are supplied with heat by the HC, using the pressure of the SA

as MV. The target temperature of the steam out of the boiler is 480 ℃. Yellow lines represent control

signals and measurements.

The dome lets out only saturated vapour, while the superheater raises the temperature

to the desired value. The heat needed is calculated with

�̇�𝐻𝑒𝑎𝑡 = �̇�(ℎ𝑂𝑢𝑡 − ℎ𝐼𝑛). Eq. (11)

where ℎ is taken from steam tables [27] and �̇� = 116 kg/s is the flow through the

system calculated with Eq. (10).

23

The heat fed into the dome and the superheater is controlled by a ratio-control

governed by a PI-controller. The ratio is decided by

ℎ𝑆𝐻

ℎ𝑆𝐷= 𝐶, Eq. (12)

where ℎ𝑆𝐻 and ℎ𝑆𝐷 are the needed specific enthalpy differences to reach saturation

temperature in the steam dome respectively 480℃ at 101 bar(a) in the super heater.

The pressure of the SA serves as measurement value with 8,5 bar(a) as SP for the HC.

A start-up sequence is added to support model simulation. The sequence is built

to give a constant heat input until a timer triggers the PI-controller to take control. It is

not considered as a real start-up sequence.

A safety pressure relieve valve (SPRV) is implemented to relief the pressure if

pressure rises above a critical pressure, which is chosen to be 109,2 bar(a). The SPRV

is implemented to give the boiler a more realistic behaviour in the sense of keeping

and supplying pressure to the steam network, which is within the scope of this thesis.

3.2.2 Backpressure Turbine

The backpressure turbine is built in three stages in Dymola: HP stage, intermediate

pressure stage and a LP stage. Each stage is modelled so that it is possible to define

the characteristics of mass flows, pressures and temperatures similar to the original

model. A Stodola turbine stage is defined by isentropic efficiency (𝜂𝑖𝑠), nominal mass

flow, nominal inlet/outlet pressure and nominal inlet temperature. The mass balance

of the turbine is calculated with

�̇�𝐻𝑃 = �̇�𝑀𝑃,𝑙𝑜𝑎𝑑 + �̇�𝐿𝑃1,𝑙𝑜𝑎𝑑 + �̇�𝐿𝑃1,𝑙𝑜𝑎𝑑 + �̇�𝑟𝑒𝑠𝑡, Eq. (13)

where �̇�𝑟𝑒𝑠𝑡 is excess steam vented from the last stage during the start-up phase of

the model. Eventually the total mass flow, �̇�𝐻𝑃, is corrected by the boiler HC during

the simulation, resulting in �̇�𝑟𝑒𝑠𝑡 = 0 (no steam is vented). The other characteristics

are set according to values in Table 2.

The sum of generated mechanical power is reduced to 97% and then 95% of

that to compensate for the mechanical and generator efficiency, respectively. This is

to simulate a more realistic yield of electricity generated. Calculations of the turbine

is mathematically done in Dymola using the Eq. (1). A screenshot of the turbine

model in Dymola is shown in Figure 27.

24

Figure 27. Overview of backpressure turbine modelled in Dymola. The valve in the upper left corner is

the turbine inlet valve.

3.2.3 Steam accumulator

The model of the SA in Dymola consists of a flash tank and a source of attemperating

water. The flash tank is the same as for the boiler dome, which has steam as the only

outflow but can take both steam and water as inflow. A screenshot of the model is

shown in Figure 28.

Figure 28. Model of steam accumulator in Dymola. The block “boundary2” is for filling the SA in if

necessary, which never were the case during this thesis.

3.2.4 Pressure Levels

Each pressure level consists of a volume simulating the total of the volumes of all the

steam pipes connected to that pressure level, see the example of MP in Figure 29. As

25

seen in Figure 29 the load is positioned inside MP pressure level. LP1- and LP2-

pressure levels are modelled in a similar way to MP pressure level.

Figure 29. The model of MP level. The SPRV is activated when the pressure of the level is above 30

bar(a). The SP for the SPRV in LP1 is 15 bar(a).

Inertia is assumed to correlate to the sensitivity of each pressure level and the ability

to sustain transients and disturbances. This is assumed because a larger volume corre-

sponds to a larger mass. The different pressure level volumes are shown in Table 4.

Table 4. Volumes of each pressure level.

Pressure level Volume P1 [𝑚3]

HP 21

MP 140

LP1 170

LP2 360

3.2.5 Attemperators

Attemperators are positioned after the superheater in the boiler and after most of the

valves. They are placed according to the original model with exceptions for the

attemperators at the SA outlet and at the MP extraction, which are removed to establ-

ish a working model. This will be affecting the temperature of MP level so that it

becomes slightly higher than that of the real plant. The slightly higher temperature

will not be affecting the results of this thesis in any measurable way. Injected water is

set at 𝑇 = 45 ℃ with the pressure of the injection point.

3.3 Transients

Two transients are used, board machine stop and the load cycle of a batch pulp

digester. These transients are used to test the performance of the two SSRC systems.

The stop transient of the board machine (KM-stop) is applied to LP1, and

causes the reduction of steam load shown in Figure 30.

26

Figure 30. The KM-stop transient for the load of LP1. The transient data originates from the plant that

is used as blueprint and therefore is not scaled.

The batch load cycle transient is applied to MP, causing the variation of steam load

shown in Figure 31.

Figure 31. The Batch cycle transient for the load of MP. The transient data originates from another

plant than the used blueprint and therefore is the transient scaled to match the models average load of

MP.

27

3.4 Building the Controllers

The SSRC systems built are Control system 1 (C1) and Control system 2 (C2). C1 is

built after the old model and C2 is built with a different priority list as concept, which

was developed during modelling. The controllers are then verified to have all desired

functions and features with one of the implemented load transients. In both C1 and C2

HP SSRC has direct signal while the other SSRCs have reverse signal. All PI-

controllers have different HLs, which give them outputs in units (kg/s) corresponding

to maximum in and out flows through the valves of the pressure levels when they are

at the desired pressures. All split outputs in the system are linearized to match the

mass flow through each of the valves that are control handles of the process.

3.4.1 Building Control system 1

C1 is built using the graphical interface of a simulator (Figure 32) as reference.

Figure 32. Graphical interface of a simulator of the reference plant for operators. The control system

has 27 splits and 6 PI-controllers. The screenshot is slightly modified from the original.

The graphical interface illustrates the splits by white and green rectangles with

rounded edges. The splits are placed from bottom to top to represent their order, first

to last, in the split structure. The bars on the side of the splits illustrate the output

magnitude of the PI-controller. The percentage boxes next to each split (either grey or

orange) indicate the magnitude of each split output. The green splits are for turbine

inlet and extractions. All the drawn lines represent LC connections. An arrow

pointing at the bottom of a split means that it is controlling a LL and an arrow

pointing at the top of a split means that it is controlling a HL.

For example, the PI-controller output of the 110-bar pressure level has an output

of 27,5%, see orange box to the upper left in Figure 32. The splits are from bottom to

28

top 45%, 10%, 10%, 58% and 0%. All the splits are illustrated in a simplified control

structure block diagram in Figure 33.

Figure 33. The block diagram shows a simplified version of C1. The control system has 16 splits and 4

PI-controllers.

The HP SSRC has a direct control signal while MP, LP1 and LP2 has reverse control

signals. The turbine is controlled by inlet pressure control.

3.4.2 Building Control system 2

The initial requirements of the new C2 were that LP2 SSRC should manoeuvre the

turbine inlet and that HP SSRC manoeuvres both inlet and outlet of the SA. Insights

from the construction and implementation of C1 lead to the concept of having the

SSRCs for MP and LP1 with a higher priority. The final version of C2 was the

product of debugging and ad hoc implementations. The control system is developed

with the philosophy that it might be more stable and energy efficient than C1. A

simplified control structure block diagram is shown in Figure 34.

29

Figure 34. The block diagram shows a simplified version of the SSRC system C2. The control system

has 14 splits and 4 PI-controllers.

The HP SSRC has a direct control signal while MP, LP1 and LP2 reverse control

signals. The turbine is controlled by backpressure control.

In addition to variating the order of splits in the split structures of the SSRCs, the

simulation capability of C2 was ensured with a few limitations:

1. LL of turbine inlet was set to 5%

2. LL of turbine extraction to MP was set to 5%

3. HL of the PI-controller for LP2 was extended by 7,87 (kg/s)

4. HL of turbine inlet was set to 42%

The limitations listed above are set to establish a control system compatible with the

model. The importance and function of these limitations are discussed further in

section 5 (“Discussion”).

3.5 Confirmation of behaviour

The behaviour of the two control systems is tested against the KM-stop transient.

Each SSRC PI-controller and split output is plotted in order to evaluate the control

system. Each SSRC controller is confirmed by how each split output behaves.

30

3.5.1 C1

The response of HP SSRC for C1 is shown in Figure 35.

Figure 35. Response to KM-stop of HP SSRC for C1. Only the HP response is shown.

The controller output (blue curve) decreases due to direct signal and decreasing

pressure. This immediately causes the signal of the MC split of turbine inlet (black

curve) to decrease. It decreases until the LLC for the valve between HP and MP starts

to increase. The increase is due to the output increase of the MC split of HP/MP in the

MP SSRC. The output is fed back as a LL for the LLC split. All other split outputs are

constant. The behaviour follows the chosen priority list.

3.5.2 C2

The response of HP SSRC for C2 is shown in Figure 36.

Figure 36. Response to KM-stop of HP SSRC for C2. Only the HP response is shown due to the large

space that many potential graphs would take.

31

The PI-controller output (blue curve) starts to increase due to increased pressure and

direct signal, and it immediately causes the signal of the MC split for the outlet of the

Steam Accumulator (magenta curve) to increase. At the same time the HLC split for

the valve between HP and LP2 decreases.

3.5.3 Tuning of the controllers

The SIMC-method was used for tuning each SSRC in the SSRC system. The

controller has different responses if a MC or a LC split is being operating during the

step response. The SIMC-method is therefore applied in the same manner for both C1

and C2 to have a more comparable result. HP SSRC is the first to be tuned, the other

SSRCs are tuned after that, in order of decreasing pressure.

The output of the SSRC to be tuned is set to constant. Then a step of fitting size

is introduced while all other SSRC in the system are active. The step is inside the

range of a MC split, directly actuating the corresponding valve. In this way the

process is equivalent to a first order process and the deadbands of the LCs are not

interacting with the step response.

The required information (illustrated in Figure 21, section 2.4.5) is estimated

after a step-response, and 𝐾𝑐 is calculated with Eq. (6) and Eq. (7). With no time

delays in the model and choosing 𝜏𝑐 = 0, the result of Eq. (8) would have been 𝜏𝑖 =

0, and therefore all 𝜏𝑖 are set to 𝜏𝑖 = 𝜏1.

During the tuning, C1 could not operate with the 𝐾𝑐 calculated with Eq. (6) and

Eq. (7). C1 did only work with 1% of the calculated 𝐾𝑐, while C2 did work with the

calculated 𝐾𝑐. This could be due to instability of the model in connection with the

simulation tool.

The control parameters of the HC in the boiler are set to 𝐾𝑐 = 0,8 and 𝜏𝑖 = 240

to simulate the longer response time of combustion.

3.6 Analysis of the Results

The objectives of the results are to state which of the two controllers is performing

better in the perspectives of energy, stability and long-term impact. The energetic

performance is evaluated by the yield of electricity generated and how much steam

that is vented during the transients. The stability performance is evaluated by check-

ing pressure trends for each pressure level against different limits, see Table 5. These

limits represent three different limits to simulate how different plants sustain pressure

transients. By using them as a reference when comparing the results of the pressure

trends, it will be easier to tell if pressure responses of C1 and C2 are within suitable

limits. Both or neither is within a specific limit. By comparing sets of limits, it is

obvious if one of the controllers is performing better than the other.

32

Table 5. The different limits and the SPRV limits of all three plants in bar(a).

P levels P1 limits P2 limits P3 limits SPRV for all

HP +- 4 +- 6 +- 6 109,2

MP +-3 +-2 +-3 30

LP1 +- 2 +- 2 +- 1,5 15

LP2 +- 1,5 +- 1,5 +- 1,5 10

Potential attrition for long-term impact is measured by the number of changes in valve

running direction during the transient. The valves are then organized into four groups,

Turbine valves (TV), PCV (for pressure reduction), Steam Accumulator valves (SAV)

and PRV (for venting). The groups represent the most desired activity first and least

desired activity last: TV, SAV, PCV and PRV. All Safety Pressure Relief Valves

(SPRV) should not intervene and therefore are not in any of these groups.

33

4 Result

Simulated results from each transient are presented in three subsections (“Energy

performance”, “Stability performance” and “Long-term impact”), while the actual

meaning of the results is discussed in later sections.

4.1 Energy performance

The yield of generated electricity and the steam vented from the system during the

transients are presented in this section for the two tested SSRC systems (C1 and C2).

4.1.1 KM-stop

Both control systems have a decreasing trend of the generated electricity after the

KM-stop is introduced, see Figure 37. The trend of C1 is smooth and stable while the

one of C2 is unstable with a recurrent shape.

Figure 37. Electricity generated by C1 and C2 during KM-stop. The unstable behaviour of C2 has a big

impact on the stability of the electricity generation.

During the KM-stop C2 is operating the SPRV of HP (Figure 38).

Figure 38. Vented steam in the HP level by C1 and C2 during KM-stop. Only C2 operates the SPRV.

34

C2 operates HP SPRV in a large-scale compared to LP2 SPRV (see the scale of the y-

axis of the graph in Figure 39). This is regarded as bad in a real plant. C1 seems to be

stable while C2 shows unstable characteristics.

Figure 39. Vented steam in the LP2 level by C1 and C2 during KM-stop. C1 is venting steam at the

beginning of the transient while C2 is venting steam almost 30 minutes after the transient starts.

4.1.2 Batch cycle

Both control systems have a recurrent trend, but there are differences. Six and a half

cycles are covered in the diagram in Figure 40. After 800 minutes the behaviour of C2

changes. A deeper low point is formed once every second batch cycle. On the other

hand, C1 has the same behaviour for all batch cycles. C1 is generally generating more

electrical power than C2.

Figure 40. Electricity generated by C1 and C2 during batch cycle load. C2 performance is not as stable

as the one of C1.

During a batch cycle both control systems are operating HP SPRV, see Figure 41.

This is regarded as bad in real processes.

35

Figure 41. Vented steam in the HP level by C1 and C2 during batch cycle load. C2 is venting a lot

more steam than C1.

During a batch cycle both control systems are venting steam from LP2. C1 is venting

more steam than C2, see graph in Figure 42.

Figure 42. Vented steam in the LP2 level by C1 and C2 during batch cycle load. C2 is barely venting

any steam from the LP2 level.

36

4.2 Stability performance

Pressure level stability performances are presented in this section. For each pressure

level there are limits, described in subsection 3.6, drawn as dashed or continuous

black lines in the diagrams.

4.2.1 KM-stop

Neither C1 nor C2 is able to suppress the KM-stop transient enough to keep the

pressure of HP within the limits set for the real plants, see the graph in Figure 43. C1

is stable while C2 is unstable. The first pressure response differs between C1 and C2:

the pressure for C1 is decreasing while the pressure for C2 is increasing.

Figure 43. The pressure response to the KM-stop of HP. It is clear that C2 is unstable.

C1 manages to suppress the KM-stop transient enough to keep the pressure of MP

within the range of P1 and P3 limits. C2 does not manage to keep the pressure within

the limits of any plant, see the graph in Figure 44.

Figure 44. The pressure response to the KM-stop of MP. C1 is close to manage to keep the pressure

within the range of the P2 limits.

Both C1 and C2 manage to suppress the KM-stop transient so that the pressure of LP1

remains within the limits of all plants, see the graph in Figure 45. C1 reaches the

higher limit of P3 but after that the trend is stable. C2 response to the KM-stop in LP1

is fast and the instability is only a small recurrent variation.

37

Figure 45. The pressure response to the KM-stop of LP1. C2 has a faster response than C1.

C1 manages to suppress the KM-stop transient within the range of all plant limits in

LP2, while C2 does not, see graph in Figure 46.

Figure 46. The pressure response to the KM-stop of LP2. C1 has a faster response than C2.

4.2.2 Batch cycle

Neither C1 nor C2 managed to suppress the batch cycle load transients enough to

keep the pressure of HP remain within the limits of the real plants, see graph in Figure

47. The graph covers six and a half cycles. The first pressure response differs between

C1 and C2: the pressure for C1 is decreasing while the pressure for C2 is increasing.

Figure 47. The pressure response of HP during batch cycle load. The trend of C1 is cyclical and stable

but outside all plant limits. The trend for C2 is unstable and is not keeping the pressure above the LLs.

C1 manages to hold all HLs of MP during all batch cycles but not all LLs. On the

other hand, C2 manages to keep the pressure within the range of the limits of P1 and

P3, see graph in Figure 48.

38

Figure 48. The pressure response of MP during batch cycle load. The response of C2 is fast but

unreliable.

For LP1 C1 exceeds all limits, while C2 remains within the margins, see graph in

Figure 49.

Figure 49. The pressure response of LP1 during batch cycle load. The response of C2 is fast and

reliable.

The LP2 pressure response of C1 to the batch cycle load transients is within the limits

while the response of C2 is above the limits for all cycles, see graph in Figure 50.

Figure 50. The pressure response of LP2 during batch cycle load.

39

4.3 Long-term impact

The results concerning the long-term impact perspective are presented in this section.

4.3.1 KM-stop

The number of changes in valve running direction for C1 and C2 during KM-stop is

shown in Figure 51. C1 is mostly manoeuvring the group of valves SAV, then the

group TV, then the group PRV and lastly the PCV. C2 is mostly manoeuvring the

group of valves PCV, then the group SAV, then the group of TV and lastly PRV.

Figure 51. The bar diagram shows how active each group of valves is during KM-stop. C1 is generally

prioritizing more desirable valve groups than C2. C2 has a five-time higher overall usage of valves

than C1.

4.3.2 Batch cycle

The number of changes in valve running direction for C1 and C2 during a batch cycle

is shown in Figure 52. C1 is manoeuvring the SAV and TV to the same extent, while

C2 is mostly manoeuvring the TV. C1 is not utilizing the PCVs at all, while C2 uses

these valves as almost one third of the actuated valves.

Figure 52. The bar diagram shows how active each group of valves are during batch cycle load. C1 is

generally prioritizing more desirable valve groups than C2. C2 has a three-time higher overall usage of

valves than C1.

62

11

74

34

107

1

36

4

0 50 100 150 200 250 300

C2

C1

NUMBER OF CHANGES IN VALVE RUNNING DIRECTION

Valve change of action during KM-stop

TV SAV PCV PRV

41

16

18

16

28

0

2

2

0 10 20 30 40 50 60 70 80 90 100

C2

C1

NUMBER OF CHANGES IN VALVE RUNNING DIRECTION

Valve change of action during Batch cycle

TV SAV PCV PRV

40

5 Discussion

This section describes and discusses the results and the thesis as a whole.

5.1 Instability

There are problems with the tuning of control systems C1 and C2. The implement-

ation of C1 was done with the SIMC-method according to the described order of

tuned SSRCs. The tuning resulted in aggressive 𝐾𝑐 coefficients for the SSRCs (all

between 1 and 20), which suggested the possibility that the method had been applied

in a wrong way. All 𝐾𝑐 coefficients were therefore changed to 1% of what the SIMC-

method estimated. All the SSRCs of C1 gave good responses according to their smo-

oth trends but the time responses were long. The tuning of C2 was done in the same

manner with 1% of the 𝐾𝑐 values that the SIMC-method estimated, but for C2 the

response time were too long. A quick choice was to let the control parameters remain

as estimated for C2 while C1 remained at 1% of it, based on the time frame of the

project. This makes the comparison between the two control systems less effective.

When the two control systems were simulated on the model for each disturb-

ance, C2 showed instability. The problem is a combination of the following factors:

• Chosen hierarchy of the SSRC • Control parameters

• Inertia in respectively pressure level • A loop among SSRCs

The hierarchy for C2 is MP, LP1, LP2 and HP. It contains a loop since LP2 operates

the turbine inlet while HP operates inlet and outlet of the SA. Here is an explanation

of the behaviour of the loop:

1. HP level has too high pressure.

a. The inlet valve of SA opens.

i. The pressure of MP decreases.

ii. The pressure of SA increases.

iii. Pressure in HP continues to be high.

2. MP level gets too low pressure.

a. The MP-extraction valve of the turbine opens more.

i. MP gets rectified.

ii. Decreasing pressure in LP1, but even more in LP2.

3. LP2 level gets too low pressure.

a. The turbine inlet valve opens more.

i. The pressure of LP2 increases.

ii. The pressure of HP is decreasing.

4. HP level gets too low pressure.

a. The SA inlet is closed while the outlet opens more.

i. The pressure of LP2 increases.

ii. The pressure of SA decreases.

5. LP2 level gets too high pressure.

a. The turbine inlet closes more.

i. The pressure of HP increases

41

6. HP level gets too high pressure and the loop is closed.

The explanation above is simplified, as most of valve actuation occurs at the same

time. Also, boiler HC will be active during the changes of pressure in the SA.

In a stable control system, which is desired, the pressure of HP level should be

rectified at 3.a.ii (4) by the turbine inlet valve that closes sooner and/or faster. This

could be done by tuning the control parameters for the HP and LP2 SSRCs. However,

the control parameters are connected to all the pressure levels inertia, which are

represented in the model by larger volumes. In the model the volume of HP differs

from the one of LP2 by a factor of 17. The difference between volumes means that

small pressure differences in LP2 (which cause the SSRC to open the turbine inlet

more) will have a greater impact on the HP level (due to the large difference of

volume). As a consequence, a small transient on the LP2 level will create a larger

transient on the HP level. This phenomenon can be used as an argument to support the

hypothesis that C2 performs better in a steam network with a lower difference

between the volumes of HP and LP2 levels.

There is a possibility that C2 can be implemented in the model without

instability characteristics through a proper tuning. For a proper tuning of a SSRC

setup, a systematic method should be developed.

5.2 Comments on results

Although C2 shows instability, the results from the simulations can be used to give

insights in SSRC “best practice”. The way in which the HP level responds to

disturbances differs in C1 and C2. In C1 the pressure of the HP level decreases, while

in C2 it increases, see Figure 43 and Figure 47. C1 response at KM-stop is explained

as follows:

1. Pressure of LP1 level too high due to board machine failure.

a. The extraction valve to LP1 closes more.

i. LP1 gets rectified.

ii. Pressure in MP increases slightly, but even more in LP2.

b. PCV to LP2 opens.

i. Pressure in LP2 increases.

2. Pressure of LP2 level gets too high.

a. The SA inlet valve opens.

i. The pressure of MP decreases.

ii. Pressure of SA increases.

b. The PRV opens.

i. LP2 gets rectified.

3. Pressure of MP level decreases.

a. The extraction valve to MP opens.

i. MP gets rectified.

ii. Pressure in HP, LP1 and LP2 decreases

4. Pressure of HP level decreases.

a. The whole system has been rectified.

42

Again, the explanation above is simplified as most of valve actuation occurs at the

same time and boiler HC will be active during changes of the pressure in the SA.

From the stability perspective C1 performs well during the KM-stop as it keeps the

pressures within all the different plants limits (except for the HP level). C2 only

succeeds in keeping the pressure of within the limits during both of the transients.

Comparing the stability of the two control setups during a batch cycle, C1 has

the better responses in HP and LP2 levels while C2 has better responses in MP and

LP1 levels. This supports the earlier stated hypothesis that C2 is fitter for a steam

network in which HP level has more inertia. C2 generally has a faster response to an

offset and this is because the factor 100 difference between the 𝐾𝑐 coefficients in the

two systems. This is affecting the stability further, but the extent is unknown.

Regarding the energy point of view, the comparison between the two control setups is

also affected by the instability of C2. It affects the graphs of generated electricity for

both disturbances, and it makes them difficult to interpret. The graph is clear enough

to state that C1 performs better and therefore no exact energy yield comparison was

calculated. Another significant factor is the position of the SPRV, which is inside the

boiler and not within the HP level. As a result, the SPRV opens at too low pressure in

the HP. Due to this position the setpoint does not match the pressure level of the HP

level. As future work, this may be compensated by changing the position of the SPRV

of by simply increasing the setpoint of the SPRV.

The usage of SPRV and PRV in the two control setups shows that both intended

hierarchies were successful. This is apparent because the priority for C1 is to sustain

the pressure at the HP level and vent steam from LP2, while the priority for C2 is to

sustain the pressure at LP2-level and release steam from the HP level. From an energy

point of view would it be desirable that the pressure of the HP level could vary more

without activating the SPRV. Less steam would be released, but the stability of the

HP level stability would be decreased, which is bad for the boiler and other units

directly connected to the HP level. Best practice would see the process varying within

the limits and sustain all steam pressure levels within the process.

The instability of C2 affects the comparisons of the long-term impact between the

control structure setups. The percentage usage of each valve group can still be

compared. For both the KM-stop and the batch cycle C1 is generally using TV and

SAV mostly, which is desired due to both these valve groups enable maximum steam

and energy usage. The results for C2 are not as reliable as the results for C1 due to the

instability. The results show that TV, SAV and PCVs are used to almost the same

extent. Potential expansion work is lost by operating PCVs whenever pressure

reductions occur. This explains why C2 is generally less energy efficient. The premise

of a loop causing the instability is followed by the logical conclusion that the valves

will be used in the same percentage extent, regardless of the total number of changes

in the valve running direction.

43

5.3 Desirable results

A few more results would be desirable to have more insights into the best practice of

SSRC structure setups, and these results would be obtained by applying:

• Variations of the SA position

• Variations of the pressure levels inertia (volumes)

Several changes in the model of the steam network would be required. Versions of the

model should first be built by changing the position of the SA between different

combinations of pressure levels. Also, each split structure should be changed accord-

ing to the position of the SA. This would provide more guidelines about how to

control steam networks with the SA in different positions.

Volume variations require new linearization of the control structures. The

results, using a comparison that is similar to the one in this work, would tell whether

C2 is a suitable SSRC structure setup for a steam network with a relatively larger HP

level. Deeper studies require a variation of all the volumes, one by one, but without an

automatic method it would be very time consuming. Writing a custom script this task

could be done in short time, but more in depth knowledge of Modelica language and

coding is required.

5.4 Limitations in setup C2 to establish a model that can be simulated

Limitations 1 to 3 (see section 3.4.2) are estimated to have a low impact on the

process and are set to establish a control system cooperating with the model. Similar

limitations are, in fact, often used in real processes. Also, limitation 4 is a common

limitation, even though not of this magnitude. It is for improving the process and

making the control system less unstable. The size of turbine inlet valves is modelled

to be large to establish a working model. The problem that occurs is that there will be

a deadband (or a slower response) above 42% of the opening degree of the inlet valve.

When the controller output is not getting any response from the process (the MV is

unchanged) the I-part will grow. The anti wind-up feature helps, but there will still be

over- and undershoots in the process. There will be overshoots if the PI-controller (in

this case the PI-controller of LP2) tries to open the valve more (no response after

42%). There will be undershoots if the PI-controller tries to close it from “fully”

opened (no response from 100% down to 42%). Before this change C2 was not

compatible with the model due to the large oscillations that were caused.

44

6 Conclusions

The built simulation test bench works, and the two SSRC systems are compared on it.

All the three perspectives evaluated conclude that C1 is the control system solution

for the model. The results indicate that C1 performs better than C2 in a pulp and paper

plant that has a HP level with low inertia. These results are pointing towards the rule

that lower inertia pressure levels should have a higher hierarchy to avoid excessive

pressure oscillations.

Other “Best practice” guidelines are listed below:

• In a plant with low inertia on HP level, rank the HP high in the hierarchy.

• In a plant with low inertia on HP level, chose inlet pressure control for the

turbine.

45

7 Future work

It is most important to develop a tuning method for SSRC systems.

The model of the steam network in “a typical pulp and paper plant” is mostly based

on an older model of an existing plant. To upgrade the model, it is suitable to

implement the features that make model behaviour closer to that of a real plant:

• New position of SPRV (alternatively higher set point)

• Dead time

• Noise

• Dynamic linearization

• Boilers control parameters

• Refine load units

As previously mentioned, the relocation of SPRV for the HP level is important.

The dead time in the system is important to implement due to the variety of

response time between different SSRC structure setups. In the case of the comparison

between C1 and C2 there would be a greater difference in the response time due to no

direct possibility of rectifying the HP level. The rectification of HP (C2) at high

pressure previously described suggests longer response times and different control

parameters.

Also noise as small disturbances and measurement uncertainty should be imple-

mented to give a better perception of how the control is affected.

The linearization should be in three stages depending on how the pressure drop

over each valve varies. In these stages of pressure drop a certain gain is active for

each individual valve, see Figure 53. This makes the control systems more dynamic

and in turn performing better.

Figure 53. The mass flow, �̇�, dependent on the pressure drop. The curve is linearized in three steps by

gains 𝐾1, 𝐾2 and 𝐾3.

Chosen control parameters for the boiler should be confirmed with literature studies

and the load unit models should be more dynamic with small errors.

Refined load units with small variations and more specific functions will make

the model more dynamic.

46

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